The area (in sq. units) of the region enclosed by the curves y=x2-1 and y=1-x2 is equal to

Question

The area (in sq. units) of the region enclosed by the curves y=x2-1 and y=1-x2 is equal to (A) (4/3) (B) (8/3) (C) (16/3) (D) (7/2)

Tardigrade Admin · Accepted Answer

y=x2-1 and y=1-x2 <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/934d16f83893334344fd697612217804-.png" /> A =∫ limits-11((1- x 2)-( x 2-1)) d x A =∫ limits-11(2-2 x 2) dx =4 ∫01(1- x 2) dx A =4( x -( x 3/3))01=4((2/3))=(8/3)

Q. The area (in sq. units) of the region enclosed by the curves $y = x^{2} - 1$ and $y = 1 - x^{2}$ is equal to

$\frac{4}{3}$

$\frac{8}{3}$

$\frac{16}{3}$

$\frac{7}{2}$

$y = x^{2} - 1$ and $y = 1 - x^{2}$

$A = - 1 \int 1 ((1 - x^{2}) - (x^{2} - 1)) d x$
$A = - 1 \int 1 (2 - 2 x^{2}) d x = 4 \int_{0}^{1} (1 - x^{2}) d x$
$A = 4 (x - \frac{x ^{3}}{3})_{0}^{1} = 4 (\frac{2}{3}) = \frac{8}{3}$

Q. The area (in sq. units) of the region enclosed by the curves y=x2−1 and y=1−x2 is equal to

34​

38​

316​

27​